Not exactly the same situation but somewhat similar. I recently adopted a great dane and I just posted about aggression between my male boxer (who's 2) and my great dane who's 1 1/2 years. My boxer was fine for the first few days then got aggressive towards my dane. I read on here about helping establish pack hierarchy.

So now I pet my boxer first, put his food down first, let him out first, let him in first, give him his treat first, and I've taught my dane to wait. Within a few days, they were best friends. It was very subtle things, small seconds of difference and it changed everything. I literally put his food bowl down 5 seconds before hers and let him get up from "waiting" 5 seconds before her. It's made a world of difference.

Also, letting them scrap it out A LITTLE isn't a bad thing. Again, it helps them establish a pack hierarchy. Of course, there are some situations where scraping it out is not okay. It just varies.